The history of geometry

Engineers, architects and people of many other professions use lines and figures in their daily work. Geometry is the branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines and angles. It must be noted that geometry is the Greek name for the science which the early Egyptians began and developed about 5000 years ago. The word geometry is derived from two Greek words: geo meaning earth and metron meaning measure. For building pyramids the early Egyptians needed professional geometers who were able to locate a line running north and south. The geometry known to the Egyptians consisted principally of rules and formulas for finding areas and volumes. The Egyptians were principally interested in the practical application of their rules.

After a time Greek philosophers and teachers developed and perfected the proofs of the Egyptians. The most important of the early Greek teachers was Pythagoras who was born about 569 before our era. He founded a school in Italy. The Students were divided into two classes – beginners and Pythagoreans. Plato, who lived more than a hundred years later than Pythagoras, was primarily a philosopher. His interest in geometry was not because of its practical use, but because of the logic contained in the proofs.

The best known name in connection with geometry is Euclid. Euclid was a teacher of geometry in Alexandria. He used to say that geometry trained the habits of expressing thoughts accurately. One of his most important textbooks is called The Elements. The Elements of Euclid has been used as a basis for all textbooks on geometry since his time. Another famous scientist of ancient times was Archimedes who lived in Sicily. Archimedes discovered many laws of mathematics.

For over twenty centuries Euclidean geometry was the ruling theory. In the 19^th century the Russian mathematician Lobachevsky founded non-Euclidean geometry of two dimensions. Such kind of geometry is called hyperbolic. It is based on the assumption that the axiom on parallels is not true, and through a point any number of straight lines can be drawn parallel to a given straight line. The third system of geometry was developed by Riemann and is called elliptic geometry. Riemann assumes that no straight line can be drawn which will not meet any other straight line. Thus we have three systems of geometry.

Task 20

Put 10 comprehension questions on the text for your groupmates to answer.

1. What

2. Why

3. When

4. Did

5. Was

6. Is

7. Who

8. How many

9. Do

10. Where

Enjoy yourself!

AT THE ZOO

One day a man went to the Zoo with a bag of nuts. He stopped near three cages of monkeys and decided to give them all the nuts in the bag. "If I divide the nuts equally among the eleven monkeys in the first cage," he thought, "one nut will remain. If I divide equally among the thirteen monkeys in the second cage, eight nuts will remain. If I divide them among the seventeen monkeys in the third cage , three nuts will remain. And if I divide the nuts equally among the forty-one monkeys in all three cages or among the monkeys in any two cages, some nuts will remain too. How can I I divide them so that none will remain?"

Could you help the man to divide his nuts among the monkeys?